A bag for blood and/or intravenous solutions and a method of making the bag are disclosed. The bag preferably comprises a polyvinyl chloride outer layer and an inner layer which is laminated to the outer layer, which covers substantially the entirety of the surface which, during use of the bag, comes in contact with blood and/or intravenous solution contained in the bag, and which is made from a material, preferably Mylar, which does not hydrolyze and/or leach into blood or intravenous solutions. Other materials may be used for both the inner and the outer layer, and the bag may be used to contain things other than blood and/or intravenous solutions.